Both sides started brightly but the home side soon seemed content to hit both Marcus Bent and Jay Bothroyd with long balls from their own half.
However, It was not until the 15th minute that the first decent chance was created; then James Beattie went closest to stealing the points in first-half stoppage time with a superb effort, which Thomas Myhre pushed over the bar.
It was Everton who were first to show after the restart. Although Charlton continued to press, too often the final choice of pass was poor. Marcus Bent almost snatched a dramatic winner during the closing stages but drove his close-range effort straight at Richard Wright.